Chapter 8.5, Problem 76E

To determine

(a)

To prove:

The graph of the equation $A{x}^2+Bxy+C{y}^2+Dx+Ey+F=0$ is a parabola if $B^2-4AC=0$.

To determine

(b)

To prove:

The graph of the equation $A{x}^2+Bxy+C{y}^2+Dx+Ey+F=0$ is an ellipse if $B^2-4AC<0$.

To determine

(c)

To prove:

The graph of the equation $A{x}^2+Bxy+C{y}^2+Dx+Ey+F=0$ is a hyperbola if $B^2-4AC>0$.